Page:Aether and Matter, 1900.djvu/47

CHAP. II] around the observer, which is carried on with him, they will be affected relative to him with the full aberrational change of direction arising from his motion, just as a moving corpuscle would be. Now the irrotational quality of aethereal motion thus pointed to, is, by Lagrange's fundamental hydrodynamical theorem, the characteristic of the motion of frictionless fluid which has been originally at rest: thus the material for a physical theory lies at hand. The aether is, as regards slow motions in bulk, simply assumed to have the properties of frictionless continuous fluid substance, while for the excessively rapid small vibrations of light it has solid elastic quality. The question remained how far these two sets of qualities can coexist in the same medium: an affirmative answer was defended, or rather illustrated, by an objective appeal to the actual properties of a substance such as pitch, which flows like water if sufficient time is allowed, while at the same time it can be moulded into an efficient tuning-fork for small vibrations as frequent as those of sound. There appears to be good ground for demurring against the mutual consistency of the properties imputed to a simple, permanent, and flawless medium like the aether being settled by an appeal to the approximate behaviour of a highly complex and viscous body like pitch: the principle that is involved can however be expressed in a purely abstract manner. If any term in the analytical dynamical equations of the aether is made up of two parts, so as to be of type such as au + bd2u/dt2 where u represents displacement, then when b is very small compared with a the first part au will practically represent the term for slow motions, while on the other hand for simple vibratory motion of excessively high frequency n, d2u/dt2 being then equal to (n/2π)2u, the second term is the all-important one. The objection to this kind of explanation, which substitutes a very close approximation for the exact term, is that we have actually to provide in the aether for a transparency which is adequate to convey the light of the most distant stars, which points rather to exact abstract mathematical relations than to complex and approximate physical laws of elasticity.

10. At the same time Sir George Stokes expressed his